Opabinia is also soft bodied, though it looks armored in the pictures, the flaps were soft. But it’s from the Carboniferous period, lots and lots later. You’re definitely not the only one to have pointed out the similarities, but Tullimonstrum (no, not making that up) is, as far as I know, still firmly in phylum Whatthehella.

Maybe someone who is not merely an enthused amateur like myself could expound.